春名 太一

We propose a mathematical model of economic agents to study origin of money. This multi-agent model is based on commodity theory of money, which says that a commodity used as money emerges from barter transaction. Each agent has a different value system which is given by a Heyting algebra, and exchanges one's commodities based on the value system. In each value system, necessity and unnecessity of commodities are expressed by some elements and their compliments on a Heyting Algebra. Moreover, the concept of the compliment is extended. Consequently, the duality of the necessity-unnecessity is weakened, and the exchanges of the commodities are promoted. The commodities which keeps being exchanged for a long time can correspond to money.

Although life is destined to be approximately described as a self-referential form, the self-reference is invalidated and life avoids a contradiction. Since life does not include any contradiction, it reveals a unity as a, whole. Since life is not a self-circulation, it implements diversity and evolvability. Here we show life as invalidated self-reference by constructing a model cell driven by damaged damage. Since life is always close to destruction. it exhibits both of the amoebic motion and the intelligent Physarum-like behavior.

Identity expressed in terms of second person descriptions is addressed in relation to robustness, and a simple computational model is proposed for preserving identity. Robustness is enhanced in the model by means of computational rules for chaotic cellular automata. The robustness enhancement mechanism is explained qualitatively. (C) 2007 Elsevier B.V. All rights reserved.

Two ideas in theoretical biology, 'decomposition into functions' and 'gluing functions', are formalized as endofunctors on the category of directed graphs. We prove that they constitute an adjunction. The invariant structures of the adjunction are obtained. They imply two biologically significant conditions: the existence of cycles in finite graphs and anticipatory diagrams. (c) 2007 Elsevier Ireland Ltd. All rights reserved.

Organization of living things is characterized by dynamical hierarchical structures inheriting discrepancy among levels. It can be expressed as a system consisting of two layers; the microscopic perspective (Extent) defined by a collection of elements and the macroscopic perspective (Intent) defined by the property as a whole, and the interplay between them. First we show that if the microscopic and macroscopic perspectives are consistent with each other (an ideal case), then the operation between the two layers can be expressed as a sheaf between a lattice and a quotient lattice, where a sheaf is a mathematical operation representing the gluing process. Second, we introduce an observer who cannot look out over the whole world, and this reveals a discrepancy between the two layers. Third, we introduce a new mathematical construction, called skeleton, that is derived by the sheaf operation. The skeleton reduces the discrepancy between the micro- and macroscopic perspectives, and that reveals the perpetual transition between the perspectives. This process yields a basic framework of biological organizations. Finally, we argue that the skeleton mediating between the two levels is a particular expression for the material cause. (c) 2006 Elsevier B.V. All rights reserved.

In this paper we concern an abstract model of self-organizing process called local cellular automata (LCA) proposed by us recently. The circular organization of living systems is addressed. A consistent circularity is defined by a closure operation on complete lattice. An inconsistent circularity is defined by a quasi-closure called weak closure implied by an internal perspective. Each cell in a LCA receives data about the time developments of its neighbors at one step before. It constructs a (in general incomplete) look-up table by taking closure (or weak closure) of the received data on an appropriate lattice. It applies obtained rule to its own present state and changes the state. In the former half of the paper, the theory which is the basis for LCA based on set lattice is reformulated in terms of complete lattice. In the latter half, we restrict cells' information receiving ability and define restricted local cellular automata (RLCA). The space-time patterns of RLCA are estimated by the variance of input-entropy over a span of time steps. The difference between closure driven RLCA and weak closure driven RLCA is discussed.

We propose a theory to formalize the indefinite features of living systems in the framework of weak topped ∩-structure. This theory contains two notions of indefiniteness, one is called external indefiniteness and the other is called autonomous indefiniteness. The former is defined as the outside of fixed points of the closure operator and the latter is defined as the difference between the set of fixed points of the weakened closure operator and a given set which defines the closure. This theory is then applied to elementary local cellular automaton (ELCA) in which the time development of its cell is driven by observing the dynamics of its nearest neighbors at the previous time step, followed by taking the closure (or the weak closure) in the appropriate space. The behavior of ELCA is characterized by its algebraic and statistical properties. In particular, we show that self-organized criticality (SOC)-like behavior appears in ELCA driven by the weakened closure operator. © 2005 Elsevier B.V. All rights reserved.